Gaze-based interaction in the gaming context offers various research opportunities. However, when looking at available games supported by eye tracking technology it becomes apparent that the potential has not been fully exploited: a majority of gaze-based games are tailored for static settings (desktop PC). We propose an experimental setting that transfers approaches of mobile gaze-based interactions to the augmented reality (AR) games domain. It is our main aim to find out if the inclusion of gaze input in an AR game has a positive impact on the User Experience (UX) in comparison to a solely touch-based approach. By doing so designers and researchers should receive insights in the design of gaze-based mobile AR games. To find answers we carried out a comparative study consisting of two mobile game prototypes. Results show that the inclusions of gaze in AR games is very well received by players and this novel approach was preferred in comparison to a design without gaze interaction.